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natulia [17]
3 years ago
10

Simplify V45 fully, giving your answer in the form avb What is the answer to this?

Mathematics
2 answers:
Sergeu [11.5K]3 years ago
7 0

\textit{Hello There!}

\text{\underline{ANSWER:}}

=3\sqrt{5} .

\textit{Hopefully, this helps you!!}

\boxed{\text{AnimeVines}}

Alexeev081 [22]3 years ago
7 0

Answer:

\sqrt{45}

\sqrt{5 \times 3 \times 3}

\sqrt{5 { \times 3}^{2} }

3 \sqrt{5}

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Whats the sum of the interior angles of a 37 gon
Zinaida [17]
Since we have a 37-gon here, the sum of the interior angles will be: 
<span>(37 - 2) * 180 </span>
<span>= 6300 degrees</span>
7 0
3 years ago
Prove each of the following statements below using one of the proof techniques and state the proof strategy you use.
pochemuha

Answer:

See below

Step-by-step explanation:

a) Direct proof: Let m be an odd integer and n be an even integer. Then, there exist integers k,j such that m=2k+1 and n=2j. Then mn=(2k+1)(2j)=2r, where r=j(2k+1) is an integer. Thus, mn is even.

b) Proof by counterpositive: Suppose that m is not even and n is not even. Then m is odd and n is odd, that is, m=2k+1 and n=2j+1 for some integers k,j. Thus, mn=4kj+2k+2j+1=2(kj+k+j)+1=2r+1, where r=kj+k+j is an integer. Hence mn is odd, i.e, mn is not even. We have proven the counterpositive.

c) Proof by contradiction: suppose that rp is NOT irrational, then rp=m/n for some integers m,n, n≠. Since r is a non zero rational number, r=a/b for some non-zero integers a,b. Then p=rp/r=rp(b/a)=(m/n)(b/a)=mb/na. Now n,a are non zero integers, thus na is a non zero integer. Additionally, mb is an integer. Therefore p is rational which is contradicts that p is irrational. Hence np is irrational.

d) Proof by cases: We can verify this directly with all the possible orderings for a,b,c. There are six cases:

a≥b≥c, a≥c≥b, b≥a≥c, b≥c≥a, c≥b≥a, c≥a≥b

Writing the details for each one is a bit long. I will give you an example for one case: suppose that c≥b≥a then max(a, max(b,c))=max(a,c)=c. On the other hand, max(max(a, b),c)=max(b,c)=c, hence the statement is true in this case.

e) Direct proof: write a=m/n and b=p/q, with m,q integers and n,q nonnegative integers. Then ab=mp/nq. mp is an integer, and nq is a non negative integer. Hence ab is rational.

f) Direct proof. By part c), √2/n is irrational for all natural numbers n. Furthermore, a is rational, then a+√2/n is irrational. Take n large enough in such a way that b-a>√2/n (b-a>0 so it is possible). Then a+√2/n is between a and b.

g) Direct proof: write m+n=2k and n+p=2j for some integers k,j. Add these equations to get m+2n+p=2k+2j. Then m+p=2k+2j-2n=2(k+j-n)=2s for some integer s=k+j-n. Thus m+p is even.

7 0
3 years ago
Simply: 200+(20-4)-2×3​
alexandr1967 [171]

Answer:

The answer is 210

Step-by-step explanation:

200+(20-4)-2x3

first you'd do 20-4= 16

then you'd do 2x3=6

next you'd 16-6=10

finally 200+10=210

5 0
3 years ago
A video store charges $5 per game rental plus $12 to rent the game system. Write an expression for renting the game system and a
spin [16.1K]
Y=5x+12
Y being the total amount and x being the number of games
3 0
3 years ago
A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time student
Butoxors [25]

Answer: (21.541,\ 23.059)

Step-by-step explanation:

The confidence interval for population mean is given by :-

\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}

Given : Sample size : n=240 , which is a large sample , so we apply z-test .

Sample mean : \overline{x}=22.3

Standard deviation : \sigma= 6

Significance level : \alpha=1-0.95=0.05

Critical value : z_{\alpha/2}=1.960

Now, a confidence interval at the 95% level of confidence will be :-

22.3\pm(1.960)\dfrac{6}{\sqrt{240}}\\\\\approx22.3\pm0.759\\\\=(22.3-0.759,\ 22.3+0.759)\\\\=(21.541,\ 23.059)

7 0
3 years ago
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